Phase algebra for analysis of hierarchical designs

ABSTRACT

A design tool can implement phase algebra based design evaluation to evaluate a circuit design with a compact representation of waveforms without simulating the individual waveforms. The tool can determine whether module instances of a register level circuit design share a common usage, each instance being associated with a mapping. Two instances share a common usage if a sequence of signal transition representations received by the first instance can be mapped using a first mapping to the same common sequence of signal transition representations as a mapping of another sequence of signal transition representations received by the second instance using a second mapping. A result sequence of signal transition representations was generated by a previous propagation of the common sequence through the common usage. If the two instances share the common usage, the result sequence is mapped to an output sequence for the second instance using the second mapping.

RELATED APPLICATIONS

This application claims priority from and is a continuation-in-part of aU.S. patent application Ser. No. 14/327,658, Attorney DocketAUS920130374US2, filed on Jul. 10, 2014, entitled “CIRCUIT DESIGNEVALUATION WITH COMPACT MULTI-WAVEFORM REPRESENTATIONS,” which isincorporated herein by reference.

This application claims priority from and is a continuation-in-part of aU.S. patent application Ser. No. 14/547,953, Attorney DocketAUS920130425US1, filed on Nov. 19, 2014, entitled “CONDITIONAL PHASEALGEBRA FOR CLOCK ANALYSIS,” which is incorporated herein by reference.

This application claims priority from and is a continuation-in-part of aU.S. patent application Ser. No. 14/547,820, Attorney DocketAUS920130424US1, filed on Nov. 19, 2014, entitled “CLOCK-GATING PHASEALGEBRA FOR CLOCK ANALYSIS,” which is incorporated herein by reference.

BACKGROUND

Embodiments of the inventive subject matter generally relate to thefield of circuit design, and, more particularly, to electronic designautomation (EDA) tools to identify potential defects in a registertransfer level (RTL) design of a chip or a system on a chip.

EDA tools are used to evaluate chip designs prior to fabrication. TheEDA process broadly consists of two steps. The first step is a check ofthe RTL design logic. The second step is a creation of a physicalcircuit design from the RTL design. The first step, checking the designlogic, can be referred to as RTL design checking. In RTL designchecking, a language such as VHDL (Very High Speed Integrated CircuitHardware Description Language) or Verilog can be used to describe andmodel the functional behavior of a circuit. RTL design checking itselfcan be decomposed into two steps. The first step is static checking andthe second step is verification, also commonly referred to as dynamicchecking. In static checking, the structure of the design is analyzedwithout simulating the behavior of the design. Conversely, inverification, the design is simulated by applying test patterns orstimulus to the inputs of the design in an attempt to exhaustivelyidentify possible errors. Verification can be an expensive process for acomplex chip or system on a chip. Verification can also be inconclusive,since it is often infeasible to apply all possible test patterns to theinputs of a complex design.

Chips and systems on chips continue to increase in complexity,comprising many systems and sub-systems. These systems and sub-systemsmight comprise multiple clock domains. A clock domain is a set ofsequential logic elements, such as transparent latches and flip-flops,and combinational logic associated with these sequential logic elementsthat are clocked by a common clock or by clocks having a commonfrequency and a fixed phase relationship. A clock signal causes a changein the state of sequential logic, such as a flip-flop or transparentlatch.

SUMMARY

Embodiments of the inventive subject matter include evaluating a circuitdesign with a compact representation of waveforms without simulating theindividual waveforms. A phase algebra based evaluation tool (alsoreferred to as the “tool”) can determine whether module instances of aregister transfer level circuit design share a common usage, eachinstance being associated with a mapping. Two instances share a commonusage if a sequence of signal transition representations received by thefirst instance can be mapped using a first mapping to the same commonsequence of signal transition representations as a mapping of anothersequence of signal transition representations received by the secondinstance using a second mapping. The common usage is associated with aresult sequence of signal transition representations that was generatedby a previous propagation of the common sequence through the commonusage. If the two instances share the common usage, the result sequenceis mapped to an output sequence for the second instance using the secondmapping.

BRIEF DESCRIPTION OF THE DRAWINGS

The present embodiments may be better understood, and numerous objects,features, and advantages made apparent to those skilled in the art byreferencing the accompanying drawings.

FIG. 1 is a conceptual diagram that depicts example phase algebra basedcircuit design evaluation with a compact multi-waveform representation.

FIG. 2 is a conceptual diagram that depicts an example hierarchy ofrelationships among data constructs.

FIG. 3 is a flowchart of example operations for initializing an RTLcircuit design representation of phase algebra based evaluation andpropagation of compact multi-waveform representations throughout thedesign representation.

FIG. 4 illustrates terminology associated with the example propagationalgorithm and pseudocode to be described.

FIG. 5 is a conceptual diagram that depicts example phase algebra basedcircuit design evaluation with a compact multi-waveform representation,including mappings of hierarchical modules with a common usage.

FIG. 6 is a conceptual diagram that depicts hierarchical modules thatare instantiated in the evaluation of the example circuit design of FIG.5.

FIG. 7 is a conceptual diagram that depicts example phase algebra basedcircuit design evaluation with a compact multi-waveform representation,including mappings of hierarchical modules without a common usage.

FIG. 8 is a conceptual diagram that depicts hierarchical modules thatare instantiated in the evaluation of the example circuit design of FIG.7.

FIG. 9 is a flowchart of example operations for initializing an RTLcircuit design representation of phase algebra based evaluation andpropagation of compact multi-waveform representations throughout thedesign representation.

FIGS. 10-12 are flowcharts of example operations for propagatingmulti-waveform representations through hierarchical modules of an RTLcircuit design representation.

FIG. 13 depicts an example computer system including a compactmulti-wave based circuit design evaluator.

DESCRIPTION OF EMBODIMENT(S)

The description that follows includes example systems, methods,techniques, instruction sequences and computer program products thatembody techniques of the present disclosure. However, it is understoodthat the described embodiments may be practiced without these specificdetails. For instance, the syntax employed to implement the disclosurecan be varied. Additionally, although illustrations refer to a flip-flopas a fundamental circuit component, embodiments need not include aflip-flop. For example, a circuit model can include transparent latchesand an inverter instead of a flip-flop as fundamental circuitcomponents. Additionally, embodiments may implement fewer operationsthan the operations described herein, while other embodiments might beimplemented with more operations than the ones described herein. Inother instances, well-known instruction instances, protocols, structuresand techniques have not been shown in detail in order not to obfuscatethe description.

Modern processors or systems on a chip include multiple components.Identifying as many design defects as possible at the static checkingphase of an RTL design check increases the efficiency of theverification process, thereby saving time and money. A circuit designtool can implement a phase algebra based evaluation tool for phasealgebra based design evaluation as described herein to efficientlyevaluate a circuit design with a compact representation of numerouswaveforms without simulating the individual waveforms. Instead ofindividual waveforms, the phase algebra based design evaluation employscompact representations of a group or set of waveforms. Phase algebrabased evaluation constructs representations of a set of waveforms basedon relationships among a devised set of functions that account for thevarious states of a signal over time. Phase algebra based evaluation canefficiently evaluate circuit designs that include hierarchical modules.

FIG. 1 is a conceptual diagram that depicts example phase algebra basedcircuit design evaluation with a compact multi-waveform representation.A circuit design tool performs phase algebra based circuit designevaluation on a machine readable circuit design representation 102 of anRTL circuit design. The circuit design representation 102 includesprimary inputs 110 and 112. A primary input is an input to the circuititself. A primary input is not driven by any component within thecircuit. Each of the primary inputs 110 (ADIN) and 112 (BDIN) representsdata signals that are provided to the circuit. The circuit design alsoincludes a clock signal GCLK 122 that is generated by a clock generatormodule instance 118.

FIG. 1 depicts the primary inputs 110 and 112 representative of theprimary inputs throughout the circuit design representation 102 for easeof understanding. Various example RTL circuit design components that canbe modeled in an RTL circuit design are described in the U.S. patentapplication Ser. No. 14/327,658, Attorney Docket AUS920130374US2, filedon Jul. 10, 2014, entitled “CIRCUIT DESIGN EVALUATION WITH COMPACTMULTI-WAVEFORM REPRESENTATIONS.”

A compact multi-waveform representation 104 is provided for the circuitdesign representation 102. For example, the compact multi-waveformrepresentation 104 is provided in a RTL description using attributes orin a file supplied as input to the circuit design tool. The circuitdesign tool determines compact multi-waveform representations generatedon nets throughout the RTL circuit design dependent upon the componentstraversed by the circuit design tool. Example compact multi-waveformrepresentations include notations “A” and “A@L”. These notations arereferred to as “phase tags” herein. This example uses a phase tag toillustrate handling of virtual clocks identified as “A”, “P”, and “G.P”.A virtual clock represents a source of transitions, such as anoscillator, that may be internal or external to the circuit design beingevaluated.

In this description, a phase tag and a phase type are distinguished. Aphase type is a construct (e.g., variable or notation) that represents ageneric virtual clock. Use of a phase type would be sufficient in adesign that contemplates a single virtual clock. A phase tag is aconstruct that identifies a virtual clock. Although a phase tag can beused in a design that contemplates a single virtual clock, the utilityof the phase tag becomes apparent when multiple virtual clocks are beingconsidered, such as a virtual clock “A” and a virtual clock “P”. Inaddition, operators associated with phase tags (“phase tag operators”)manipulate results of phase type operators as appropriate for multiplevirtual clocks. The particular terminology used to distinguish theseconstructs should not be used to limit claim scope. For thisillustration, the notation “A” represents a set of signals or waveformswith a clock signal behavior corresponding to a virtual clock A. Thenotation “A@L” represents a set of signals or waveforms corresponding toa latch clocked by the leading edge of the virtual clock identified asA. Similarly, the notation “B” would represent a set of signals orwaveforms with a clock signal behavior corresponding to a virtual clockB.

The circuit design representation 102 includes a clock generator moduleinstance 118, flip-flop module instances 124 and 126, and an inverter128. A net 134 is graphically depicted as connecting output of theprimary input 110 to an FD input of the flip-flop module instance 124. Anet 136 is graphically depicted as connecting output of the primaryinput 112 to an FD input of the flip-flop module instance 126. A net 122is graphically depicted as connecting output of the clock generatormodule instance 118 to an FCLK input of the flip-flop module instance126 and the input of the inverter 128. A net 130 is graphically depictedas connecting output of the inverter 128 to an FCLK input of theflip-flop module instance 124. It is well understood in the field ofcircuit design that a module instance is the inclusion of a first modulewithin a second module by reference, so that the first module's contentscan be reused without duplication.

The phase algebra based evaluation tool (also referred to as the “tool”or the “evaluation tool”) determines that inputting the compactmulti-waveform representations denoted by the notations “M->A@L:0” 114and “˜G.P” 132 (which corresponds to a compact multi-waveformrepresentation “G.P” 125 after being propagated through the inverter128) into the flip-flop module instance 124 will yield a compactmulti-waveform representation with a notation of “M->G.P@TPGF:0” 142.The phase algebra based evaluation tool also determines that inputtingthe compact multi-waveform representations denoted by the notations“N->0:P@T” 116 and “G.P” 125 into the flip-flop module instance 126 willyield a compact multi-waveform representation with a phase expressionnotation of “N->0:G.P@LPGF” 144. The phase algebra based evaluation toolpropagates compact multi-waveform representations throughout nets of thecircuit design representation 102 using look up tables constructedbased, at least in part, on a set of possible waveform states, asdescribed in the U.S. patent application Ser. No. 14/327,658, AttorneyDocket AUS920130374US2, filed on Jul. 10, 2014, entitled “CIRCUIT DESIGNEVALUATION WITH COMPACT MULTI-WAVEFORM REPRESENTATIONS” and the U.S.patent application Ser. No. 14/547,953, Attorney Docket AUS920130425US1, filed on Nov. 19, 2014, entitled “CONDITIONAL PHASE ALGEBRA FORCLOCK ANALYSIS.”

The circuit design representation 102 of FIG. 1 depicts several modulesarranged in hierarchical order. A hierarchical module “TOP” 108 includesthe flip-flop module instance F1:FLOP 124, the flip-flop module instanceF2:FLOP 126, and the clock generator module instance 118. The flip-flopmodule instances F1:FLOP 124 and F2:FLOP 126 are each separate instances(i.e., instances F1 and F2) of a flip-flop module FLOP, such as of aflip-flop module 602 of FIG. 6. The clock generator module instanceG:CLKGEN 118 is an instance (i.e., instance G) of a clock generatormodule CLKGEN, such as of a clock generator module 604 of FIG. 6. Thedescription below describes various embodiments of how the phase algebrabased evaluation efficiently evaluates hierarchical circuit designs thatincludes the top level module 108 and module instances 118, 124, and126.

Regarding FIG. 1, the circuit design representation 102 also includesseveral modes. A mode is a Boolean function of the value of a signal ina circuit, referred to as a mode signal. A mode signal can be used toselect between a first signal and a second signal, where the secondsignal is different from the first signal. The modes of the circuitdesign representation 102 are depicted using phase expressions, whichare a higher level construct from phase tags, i.e., a phase expressionincludes one or more phase tags (or a higher level construct calledMIPES that are based on the phase tags) that are joined by a modeexpression. The use and nomenclature of the constructs used to representcompact multi-waveform representations is described below with referenceto FIG. 2.

One mode of the circuit design representation 102 is depicted by a phaseexpression “M->A@L:0” 114. The phase expression “M->A@L:0” 114 indicatesthat the phase expression 114 can be either an “A@L” or a “0” dependingon the value of the Boolean function represented by the mode expression“M”. For example, the phase expression “M->A@L:0” 114 indicates that thephase expression 114 can be an “A@L” if the Boolean function representedby the mode expression “M” evaluates to the value true, and can be a “0”if the Boolean function represented by the mode expression “M” evaluatesto the value false. Other interpretations are possible.

A mode of the circuit design representation 102 is further depicted bythe phase expression “N->0:P@T” 116. The phase expression “N->0:P@T” 116indicates that the phase expression 116 can be either a “0” or a “P@T”depending on the value of the Boolean function represented by the modeexpression “N”. For example, the phase expression “N->0:P@T” 116indicates that the phase expression 116 can be a “0” if the Booleanfunction represented by the mode expression “N” evaluates to the valuetrue, and can be a “P@T” if the Boolean function represented by the modeexpression “N” evaluates to the value false. Other interpretations arepossible.

In FIG. 1, module TOP 108 contains three instances of other modules: twoinstances of module FLOP, named F1 124 and F2 126, and one instance ofmodule CLKGEN named G 118. Each instance is represented by a box in thediagram, also referred as an instance box. The label associated with thebox for the flip-flop module instance 126 indicates both the instancename F2 and name of the module being instantiated FLOP. The module FLOP(e.g., module FLOP 602) being instantiated is referred to as thedefining module of the flip-flop module instance 126. The module TOP 108containing the flip-flop module instance 126 is referred to as theinstantiating module of the instance.

The term box refers to either an instance box or a primitive component(also called a primitive box). In one embodiment, the points at whichboxes connect to signals are called pins. Ports are points at whichsignals connect to the external interface of a module. Thus, pins of aninstance box correspond to ports of its defining module. The instancebox for the module F1:FLOP 126 in module TOP 108 includes pins named FD,FCLK, and FQ, which correspond to the ports that have the same name inthe defining module FLOP (e.g., FLOP module 602 of FIG. 6). For example,the signal ADIN 134 is connected to input pin FD of the instance box ofthe flip-flop module instance 124, which corresponds to input port FD ofthe module FLOP (e.g., module FLOP 602).

The circuit design representation 102 includes hierarchical modules 108,124, 126, and 118. Typically, each such module has a unique module name,and includes named input and output ports through which it communicateswith parts of the design outside the module. Thus, a hierarchical designconsists of multiple modules organized into a hierarchy throughinstantiation, or through including one module within another byreference. Such a reference is called a module instance.

As described above, the phase expressions 114 and 116 specify sets ofwaveforms. Specifically, the string “G.P” of phase expression 125specifies that the net will have the waveform of virtual clock P ofinstance G. The conditional phase expression “M->A@L:0” 114 indicatesthat when mode M is active, that input receives transitions launched bythe leading edge of virtual clock A. Otherwise, the input is held low(constant 0). The phase expression 114 is conditional upon an operatingmode of the design. Similarly, the phase expression “N->0:P@T” 116indicates that when mode N is active, that input is held low. Otherwise,the input BDIN receives transitions launched by the trailing edge ofvirtual clock P. The virtual clock P of the phase expression “N->0:P@T”116 (received by the module TOP 108) is not the same virtual clock asthe virtual clock P of the phase expression “G.P” 125 generated bymodule instance G.CLKGEN 118 (referenced by the module CLKGEN), as thesevirtual clocks have different scope. In a hierarchical design, all nameswithin modules have local scope, meaning that the binding of the name toan object only applies within the module. This applies to instancenames, signal names, and to the names of virtual clocks and modes.

In one embodiment, the phase expressions can be propagated through thehierarchical modules of the circuit design representation 102 byflattening the circuit design representation 102. After the circuitdesign representation 102 that includes hierarchical modules isflattened, the circuit design representation 102 replaces each instanceof a module with the contents of its defining module. The flattenedcircuit design representation of the circuit design representation 102includes a copy of each primitive box and signal defined within a modulefor each global instance of that module.

In other embodiments, instead of flattening the circuit designrepresentation 102, propagation of phase expressions through certainmodules is reused for multiple instances, resulting in a more efficientand faster propagation of phase expressions through the circuit designrepresentation 102. The embodiments described below specify how two setsof phase expressions (114 and 132 for the first instance 124, and 116and 125 for the second instance 126) that are propagated to the inputsof the two module instances 124 and 126 of the module FLOP are “mappeddown” to a single set of phase expressions at the input ports of adefining module for the module FLOP. The single set of phase expressionsis then propagated through the defining module for the module FLOP. Aresult of a single set of phase expressions is then “mapped up” at theoutput ports of the defining module for the module FLOP, resulting intwo separate phase expressions 142 and 144 that are the outputs of thetwo module instances 124 and 126. In other words, the phase expressionsfor both of the instances 124 and 126 of the flip-flop module arepropagated through the contents (primitive components) of the flip-flopmodule only one time, instead of being propagated twice (once perinstance) in a flat model of propagation.

The phase algebra based evaluation tool propagates the phase expressions114, 116, 125, and 132 through the module instances 124 and 126 of thecircuit design representation 102 to generate the phase expressions 142and 144. The manner in which the phase tags and phase expressions arepropagated through the circuit design representation 102 is described inmore detail below.

When compact multi-waveform representations have been determined, achecking unit 106 of the evaluation tool analyzes the compactmulti-waveform representations associated with the nets of the circuitdesign representation 102. The checking unit 106 can identify defects inthe design using these compact multi-waveform representations. Forexample, the checking unit 106 can evaluate the transition behaviorrepresented by a compact multi-waveform representation associated with anet against a rule or constraint of the net. The rule or constraint ofthe net can be explicit (e.g., directly defined in associated with thenet) or implicit (e.g., indirectly associated with the net via acharacteristic of the net or at least one of the sinks of the net). Forexample, the phase expression outputs generated in FIG. 1 (e.g., outputs142 and 144) can be provided to the checking algorithms (such asdescribed with reference to patent application Ser. No. 14/547,953,Attorney Docket AUS920130425US1) to detect characteristics associatedwith the design.

A previous state of a signal can be related to multiple possible nextstates of the signal with a compact representation. Each of theserelationships is referred to herein as a nondeterministic transitionfunction (“NTF”). The mapping of time to NTFs can be referred to as awaveform set function (WSF). Each NTF relates a previous state of awaveform or set of waveforms to a set of possible next states. Althoughseparated by a few layers of constructs, the compact multi-waveformrepresentations mentioned earlier are based upon sequences of theseNTFs. The NTFs, which can be considered the building blocks, will befirst described. Constructs that build upon these NTFs will then bedescribed. FIG. 2 depicts an example hierarchy of dataconstructs/objects built upon NTFs revealing relationships between thepreviously mentioned phase tags and NTFs. FIG. 2 will be explored inmore detail after describing the data constructs individually. Variousexample NTFs are described in the U.S. patent application Ser. No.14/327,658, Attorney Docket AUS920130374US2, filed on Jul. 10, 2014.

When propagating compact multi-waveform representations throughout adesign, the compact multi-waveform representations are decomposed intothe NTFs in order to apply the appropriate NTF operators upon theconstituent NTFs. The NTF operators correspond to operations of circuitcomponents (e.g., ntf_and that corresponds to an AND operation of NTFs)and some operations employed for coherency (e.g., ntf_fix_adjacent andntf_is_subset). The operations can be implemented with look ups, becausethe look up tables are constructed based on the signal behaviorrepresented by the NTFs and the foundational functions that capturetransitional behavior.

Each phase type can be considered a construct (e.g., variable ornotation) that represents a set of waveforms as a function of anon-specific virtual clock, as mentioned above. A phase type grouprepresents one or more phase types. For example, the phase type groupGCE represents a grouping of two phase types. Phase type groups can beused to differentiate among phase types that have the same ClockedWaveform Set Specification (CWSS).

Phase type operators operate upon the higher level construct of phasetypes by invoking the operators of lower level constructs. Since phasetypes correspond to sets of waveforms, the phase type operatorsrepresent operations on sets of waveforms. Each phase type is associatedwith a CWSS and a phase type group. Each CWSS is comprised of NTFs. EachNTF is based upon a WSF, which, in turn, represents a set of multiplewaveforms. The phase type group operators can be identified by examplefunction names. The phase type group operators indicate possible outputreferred to herein as meta phase type groups (meta-PTGs). A meta phasetype group is a grouping of phase type groups. Meta phase type groupsare implemented to specify results of phase type group operations thatconform to the rules specified herein. Phase type groups allow for thecompact representations of multiple waveforms because the groupidentifiers can be used to disambiguate a sequence of nondeterministicsignal transition representations that map to multiple phase types.

FIG. 2 is a conceptual diagram that depicts an example hierarchy ofrelationships among data constructs. Depending on the programminglanguage and particular literature, a data construct can be referred toas a class, an object, a structure, etc. This example data construct 200includes several elements or members that define the structure of theclass and behavior of the class. The structure of this data construct200 is defined by the following members: NTFs 208, CWSSs 216, phase typegroups 220, meta phase type groups 224, phase types 232, phase tags 236,mode expressions 240, mode independent phase expressions (MIPEs) 244,phase expressions 248, reduced orthogonal list of condition-MIPE pairs(ROLCMPs) 222, and phase ids 226. The behavior of the data construct 200is defined by functions or operators that operate on the depictedmembers: NTF operators 260, CWSS operators 264, phase type groupoperators 268, phase type operators 272, phase tag operators 276, modeoperators 280, MIPE operators 284, phase expression operators 288, andphase id operators 292.

FIG. 2 depicts a waveform set function (WSF) 204 as supporting the NTFdata construct 208. The WSF 204 is depicted with a dashed line becausethe WSF 204 may not be explicitly defined in a data construct. An NTFdata construct can be defined in a class, for example, based onassumptions that rely upon a WSF without explicitly indicating themappings from each unit of time to an NTF.

A CWSS 216 is a sequence of NTFs 208. Together with a virtual clock 212,a CWSS 216 defines sets of waveforms 228. The virtual clock 212 is alsodepicted with a dashed line because this may not be explicitly definedin a data construct. The information for a virtual clock (e.g., timingparameters) can be assumed or implied by the CWSS data construct 216.The NIT operators 260 manipulate each NTF 208 that comprises an instanceof a CWSS 216, thereby manipulating the CWSS 216 instance.

A user can apply phase tags 236 or phase expressions 248 to the primaryinputs and the outputs of clock generators in a circuit design.Operations (i.e., phase tag operators 276 or phase expression operators288) are performed on these phase tags 236 or phase expressions 248.When the operations are performed, the phase tags 236 or phaseexpressions 248 are propagated throughout a design, and the resultingphase tags 236 or phase expressions 248 can be analyzed to identifypossible design defects or particular design characteristics. A phasetag 236 or phase expression 248 is propagated throughout the circuitdesign by transforming input phase tags or input phase expressionsreceived at primary inputs and outputs of clock generators in a circuitdesign through the previously discussed look up tables so that each netof the circuit design is associated with a phase tag 236 or phaseexpression 248.

A phase type 232 is a generalized version of a phase tag 236. While aphase tag 236 can be associated with a particular virtual clock 212, aphase type 232 is a generalized expression representing a set ofwaveforms 228 with respect to any virtual clock. As with the othervariable types, a phase type 232 can be manipulated through phase typeoperators 272. A phase type 232 is associated with a clocked waveformset specification (CWSS) 216 and a phase type group 220.

As previously mentioned, multiple phase types 232 can be associated withthe same CWSS 216. A phase type group 220 distinguishes such phase types232, and can distinguish characteristics of signals represented by phasetypes 232, such as clock signals as compared to data signals. Certainphase type groups 220 can be constituent elements of a meta phase typegroup 224. Phase type groups 220 and meta phase type groups 224 can bemanipulated through phase type group operators 268.

Phase tags 236 and phase expressions 248 themselves are comprised oflower level data constructs (e.g., CWSSs) and also can be converted intodifferent data constructs on which operations are executed. A phaseexpression 248 is comprised of zero or more mode expressions 240 and oneor more MIPEs 244.

A mode expression 240 represents a condition in which a design canoperate among multiple modes. A mode is a Boolean function of the valueof a signal in the design. A mode can represent a selection between afirst signal and a second signal that is different from the firstsignal. For example, a design might include a dual input multiplexer. Afirst input to the multiplexer might be a first clock signal and asecond input to the multiplexer might be a second clock signal that isasynchronous to the first clock signal. The multiplexer can receive aselector signal that causes it to select between the first signal andthe second signal. In the example of FIG. 1, the design includes severalmodes (e.g., mode M of the phase expression “M->A@L:0” and mode N of thephase expression “N->0:P@T”), each of which can be represented via amode expression 240. Operations can be performed on the mode expressions240 through the mode operators 280.

A MIPE 244 is comprised of one or more phase tags 236. A MIPE 244represents a set of waveforms 228 that is a function of the sets ofwaveforms 228 represented by the constituent phase tags 236 of the MIPE244. Operations can be performed on a MIPE 244 through the MIPEoperators 284.

A phase expression 248 can be converted into a reduced orthogonal listof condition-MIPE pairs 222, designated as a ROLCMP 222. A ROLCMP 222 isa data construct that enables phase expressions 248 to be converted intophase ids 226. A phase id 226 is a numerical handle associated with aphase expression 248, enabling phase expressions 248 to be more easilymanipulated. Subsequent sections of this specification describeconvening a phase expression 248 into a ROLCMP 222, and converting aROLCMP 222 into a phase id 226.

A phase tag 236 represents a set of waveforms 228 via CWSSs. In somecases, a phase tag 236 can be associated with a virtual clock 212.Syntactically, if a phase tag 236 is associated with a virtual clock212, the phase tag will follow a syntax which includes the name of thevirtual clock 212. One such syntax can be represented as “ClockName@Type of Clock Signal.” For example, the phase tag 236 having avalue of “A@L” designates the waveform set 228 associated with a latchclocked by the leading phase of virtual clock “A.” However, in othercases, a phase tag 236 may not be associated with a virtual clock 212.For instance, the phase tag 236 having a value that includes “*”designates the set of all possible waveforms 228. Phase tags 236 can bemanipulated via phase tag operators 276. Phase tag operators 276implement operations on phase tags 236. A phase tag 236 can be employedto distinguish among a type of signal, such as whether a signal is aclock signal, a data signal (e.g., latch driven signal), or a constant;a type of clock, such as a level, pulse, or delayed clock and invertedversions of each; and a phase of data, such as leading, trailing, or acombination.

As mentioned earlier, a phase type 232 is a generalized expressionrepresenting a set of waveforms 228. For example, a phase tag 236 havinga value of “A@L” can be generalized to the phase type “C@L,” whichrepresents a set of waveforms 228 associated with aleading-phase-clocked latch clocked by any clock C. In some instances, aphase tag 236 conflates with the concept of a phase type 232.

As discussed above, more than one phase type 232 can be represented byidentical CWSSs 216. Phase type groups 220 can distinguish phase types232 that are represented by identical CWSSs 216. Phase type groups 220can also be implemented to distinguish among classes of signals, such asclock signals, data signals, and combinations of clock and data signals.

Phase expressions 248 can be comprised of mode expressions 240 and MIPES244. A mode expression 240 is a Boolean function with a mode as itsargument. As discussed above, a mode is a Boolean function of the valueof a signal in a design. For instance, if a design includes a dual inputmultiplexer, wherein a first input is a first clock signal and a secondinput is a second clock signal and a selector signal to the multiplexercauses the multiplexer to select the first or the second clock signal,then a mode expression 240 can represent the conditionality of themultiplexer's output, i.e., that it is either the first clock signal orthe second clock signal depending on the selector signal received at themultiplexer. Syntactically, a mode expression 240 can be specified inBackus-Naur form:

<mode_expression> ::= <mode_and_expression> | <mode_expression> “|”<mode_and_expression> <mode_and_expression> ::= <mode_prefix_expression>| <mode_and_expression> “&” <mode_prefix_expression><mode_prefix_expression> ::= <mode_primary_expression> | “~”<mode_prefix_expression> <mode_primary_expression> ::= <mode> | “0” |“1” | “(“<mode_expression>”)”.

The mode operators 280 comprise the logical functions NOT, AND, OR, andXOR that can take mode expressions 240 as inputs to generate an outputmode expression 240 that has been manipulated via operation of one ofthe logical functions. For example, a logical function AND can beapplied to values of two selection signals.

A MIPE 244 is a string that is comprised of a single phase tag 236 ormultiple phase tags 236. In particular, a multi-phase tag 236 MIPE 244is an expression in which two or more phase tags 236 are joined by atransition-union operator, denoted with the “̂” symbol. A MIPE 244represents a set of waveforms 228 that is a function of the set ofwaveforms 228 represented by the constituent phase tags 236.Specifically, a MIPE 244 represents the set of all waveforms 228 thathave transitions only at times coincident with the times of transitionsof waveforms in the sets of waveforms 228 represented by the constituentphase tags 236. Syntactically, a MIPE 244 can be expressed inBackus-Naur form:

<mode_independent_phase_expression> ::= <phase_tag> |<mode_independent_phase_expression> “{circumflex over ( )}” <phase_tag>.For example, the MIPE “A@L ̂ B@L” means the set of waveforms that cantransition from the leading edge of either clock A or clock B. The MIPEoperators 284 allow operations to be performed on MIPES 244.

Phase expressions 248 model the behavior of designs in which at leastone circuit component receives a first clock signal and a second clocksignal, wherein the first clock signal is asynchronous to the secondclock signal. Additionally, phase expressions 248 model the behavior ofdesigns in which at least one circuit component is capable of selectinga first signal or a second signal.

Syntactically, a phase expression 248 can be expressed in Backus-Naurform as follows:

<phase_expression> ::= <mode_independent_phase expression>|<conditional_phase_expression> <conditional_phase_expression>:: =<mode_expression> “−>” <mode_independent_phase_expression> “:”<phase_expression>.

The relationship between a phase expression 248 and the set of waveforms228 that the phase expression 248 represents is best understood throughan example. Consider the example phase expression 248 pe3=m->pe1:pe2,where m is a mode expression 240, pe1 is a MIPE 244, and pe2 is a phaseexpression 248. The set of waveforms that phase expression pe3 specifiesis the set of waveforms w3 such that, for some w1 waveform in pe1 andsome w2 waveform in pe2, w3(t)=w1(t) if m is true at time t; otherwise,w3(t)=w2(t). Two phase expressions 248 are equal if the waveform set 228that each phase expression 248 specifies is the same. In some instances,a phase expression 248 might be optimally expressed in reducedorthogonal form. For example, the phase expression 248pe=m_(—)1->p_(—)1:m2->p_(—)2: . . . :p_k is in a reduced orthogonal formif four conditions are met: the m_i mode expressions 240 are pairwiseorthogonal, meaning that m_i & m_j=0 whenever i does not equal j; noneof the m_i mode expressions 240 are constant false Boolean functions,meaning that there does not exist an m_i that equals 0; the modeexpression 240 defined by m_k=˜m_(—)1 & ˜m_(—)2 & . . . & ˜m_{k−1} isnot the constant false Boolean function, meaning that m_k does not equal0; and the p_i MIPEs 244 are different from each other.

The phase expression operators 288 implement mathematical operations(i.e. logical operations) on phase expressions 248. For example, thephase expression operators 288 can be used to find the logical AND of afirst phase expression 248 and a second phase expression 248. Ingeneral, phase expression operators 288 perform operations on phaseexpressions 248.

The following flowcharts provide example operation of a phase algebrabased design tool that operates with compact multi-waveformrepresentations. These example operations will refer back to theoperators and data constructs described herein, and also as described inthe tables in the U.S. patent application Ser. No. 14/327,658, AttorneyDocket AUS920130374US2.

FIG. 3 is a flowchart of example operations for initializing a circuitdesign representation of phase algebra based evaluation and propagationof compact multi-waveform representations throughout the designrepresentation. At block 302, a representation of multiple waveforms isreceived at each primary input and at the output of each clock generatorof a circuit design representation. For instance, a phase tag or phaseexpression is associated with a primary input of a circuit designrepresentation. At block 304, the circuit design representation isinitialized to prepare the circuit design representation to acceptpropagated multi-waveform representations. The initialization marks netsfor propagation operations. At block 306, the multi-waveformrepresentations are determined for each of the nets in the RTL circuitdesign resulting from the received multi-waveform representation. Forexample, operators are applied to determine output phase tags based onthe various circuit components modeled in the circuit designrepresentation. At block 308, the determined multi-waveformrepresentations are supplied for evaluation of the RTL circuit design.

As discussed earlier, higher level data constructs (e.g., phase tags)are decomposed into lower level data constructs (e.g., NTFs) in order toapply operations of circuit components modeled in the circuit designrepresentation. These operations often yield a sequence of NTFs or aCWSS that is converted back into a phase type in order for propagationto continue or determine an output to associate with a net for laterdefect analysis. An output phase type can be determined based on areceived input CWSS and a received input phase tag group or meta phasetag group.

FIG. 4 illustrates terminology associated with the example propagationalgorithm and pseudocode to be described. A flip-flop 408 and path delayblock (PDB) 416 are referred to as boxes. The connectors 404, 412represent nets. The boxes 408, 416 can also be referred to as nodes. Theconnector 404 is the input net to a flip-flop 408, and the connector 412(“netA”) is both the output net from the flip-flop 408 and the input netto the PDB 416. The propagation algorithm determines an output phase id,which will appear at netA 412. PDB 416 can be referred to as the sinkbox of netA 412. In one embodiment, a source set and an update set canbe established. The source set and update set can be data structuresthat store information about the status of each box in a circuit designrepresentation. For example, the source set might include boxes that areto be processed by the current iteration of the propagation algorithm.The update set can include boxes that are to be processed by the nextiteration of the propagation algorithm. Various embodiments of thepropagation algorithm are described below with reference to FIGS. 10-12and the pseudocode.

FIG. 5 illustrates one embodiment of propagating a single set of phaseexpressions through a single instance of a flip-flop module. A circuitdesign representation 502 of FIG. 5 is similar to the circuit designrepresentation 102 of FIG. 1, except that mappings for each of theflip-flop module instances 524 and 526 are shown. Thus, the circuitdesign representation 502 includes a clock generator module instance518, flip-flop module instances 524 and 526, and an inverter 528. A net534 is graphically depicted as connecting output of the primary input510 (ADIN) to an FD input of the flip-flop module instance 524. A net536 is graphically depicted as connecting output of the primary input512 (BDIN) to an FD input of the flip-flop module instance 526. A net522 is graphically depicted as connecting output of the clock generatormodule instance 518 to an FCLK input of the flip-flop module instance526 and the input of the inverter 528. A net 530 is graphically depictedas connecting output of the inverter 528 to an FCLK input of theflip-flop module instance 524.

As virtual clocks and modes are local in a hierarchical design, theevaluation tool generates new virtual clocks and/or new modes formodules that do not have defined virtual clocks and/or modes. The phasealgebra based evaluation tool thus can generate the new virtualclock/mode (referred to as deriving a virtual clock/mode) for a module.The phase algebra based evaluation tool can also generate a new phaseexpression for the module that refers to the derived virtual clock ormode. This process occurs at module boundaries, i.e., either at theinput port of a module, or at the output pin of an instance box. Moduleinstances 124, 126, and 118 do not have defined virtual clocks/modes, asthey are instantiated from the defining modules FLOP and CLKGEN.

The defining modules are shown in FIG. 6 as module FLOP 602 and moduleCLKGEN 604. Thus, with reference to FIG. 6, the tool can derive virtualclocks ̂C1 and ̂C2 and one derived mode ̂M1 for the module FLOP 602(where the “̂” notation indicates a derived clock or mode that is localfor a given module). The defining module CLKGEN 604 already includes adesigner-specified “P” virtual clock. The tool does not derive a virtualclock for the module CLKGEN 604. During propagation of phase expressionsthrough the defining module 602, the phase expressions (as received onFD 606 and FCLK 608 input ports) are propagated through a flip-flopcomponent 612 to generate a phase expression on an output port FQ 610. Aclock generator component 622 generates a clock signal that ispropagated as a CLK 624 through output port 620, such as described inU.S. patent application Ser. No. 14/327,658, Attorney DocketAUS920130374US2.

Once the two virtual clocks (̂C1 and ̂C2) and the mode (̂M1) are derived,the tool can generate a mapping for each of the hierarchical moduleinstances 524, 526, and 518. Thus, the tool generates a mapping 550 forthe flip-flop module instance 524, a mapping 560 for the flip-flopmodule instance 526, and a mapping 570 for the clock generator moduleinstance 518. Each of the mappings 550, 560, and 570 is a one-to-onefunction associated with an instance box that maps the virtual clocksand modes in the instantiating module of the instance box to the virtualclocks and modes in the defining module of the instance box, orinversions thereof.

The tool also can generate mappings for any first instances of moduleswhere a given circuit design representation includes multiple instancesof the same module. Thus, the tool can first generate the mapping 570for the first and single instance 518 of the CLKGEN module and themapping 550 for a first instance 524 of the multiple-instance FLOPmodules 524 and 526. The tool then generates the mapping 560 for thesecond instance 526 of the multiple-instance FLOP modules 524 and 526such that the mapping 560 is compatible with the mapping 550. Twomappings for two instances of the same module are compatible with eachother if the phase expression(s) associated with both of the twoinstances of this module can be propagated once through the definingmodule and generate an output phase expression that can then be mappedup to two separate phase expressions. Two mappings for two instances ofthe same module are compatible with each other if an input sequence ofsignal transition representations received by the first instance can bemapped, using a first mapping, to the same common sequence of signaltransition representations as a mapping of another input sequence ofsignal transition representations received by the second instance usinga second mapping.

Given a virtual clock and mode map at an instance box, the tool cantransform a phase expression in the instantiating module into a phaseexpression in the defining module, or vice versa. The tool can map thephase expression by the following procedure:

1. For each clock-dependent phase tag in a phase expression, the toolreplaces a virtual clock of that phase tag by the virtual clock to orfrom which it is mapped. If the mapping is through an inversion, thenthe tool can apply a phase inversion function to the phase tag. Thephase inversion function replaces an input phase tag with the phase tagthat would be produced by inverting the virtual clock referenced by theinput phase tag. For example, applying the phase inversion function tothe phase tag “P” would produce the phase tag “˜P”, and applying thephase inversion function to the phase tag “P@L” would produce the phasetag “P@T”.

2. For each conditional phase expression (i.e., that contains a modeexpression), the tool replaces each mode by the mode to or from which itis mapped. If the mapping was through an inversion, then the tool canswap the if-true and if-false branches of the conditional phaseexpression.

3. The tool can perform the mapping as long as a phase expression doesnot reference virtual clocks or modes that are not in the map.

The process of mapping a phase expression from the instantiating moduleto the defining module is referred to as mapping down the phaseexpression. The process of mapping a phase expression from the definingmodule to the instantiating module is referred to as mapping up thephase expression. A phase expression in an instantiating module isconsistent with a phase expression in a defining module, or vice versa,if one is equivalent to a mapping of the other.

The mapping 550 includes a mapping of “A->̂C1”, “G.P->˜̂C2”, and “M->̂M1”.The mapping 550 can be used to map down the instantiating module phaseexpressions “M->A@L:0” and “˜G.P”. The mapping 550 maps theinstantiating module phase expressions to the defining module phaseexpressions “̂M1->C1@L:0” and “̂C2”, respectively. Similarly, the mapping560 includes a mapping of “P->˜̂C1”, “G.P->̂C2”, and “N->˜̂M1”. The mapping560 can be used to map down the instantiating module phase expressionsof “N->0:P@T” and “G.P”. The mapping 560 maps the instantiating modulephase expressions to the defining module phase expressions “̂M1->C1@L:0”and to “̂C2” (which are referred to as a common sequence of signaltransition representations), respectively. In this example, the mappings550 and 560 both can be used to map up the same defining module phaseexpression (i.e., the same common sequence). In other words, theinstances 524 and 526 have the same input phase expression signature,where the input phase expression signature is the common sequence ofsignal transition representations. The input phase expression signaturecan be represented as a table, as shown by element 650 (of FIG. 6),where column 652 includes the ports of the defining module 602, andcolumn 654 maps each of the phase expressions “̂M1->C1@L:0” and “̂C2” toeach port of the defining module 602.

Once the mappings 550, 560, and 570 are generated, and the tooldetermines that the phase expression only needs to be propagated throughone instance of FLOP, the phase expressions are then propagated throughmodule FLOP. Specifically, the phase expression at the output of theflip-flop in FLOP is equal to the result of propagating the phaseexpressions at its inputs, “̂M1->C1@L:0” and “̂C2”, using the phaseexpression operator 288 corresponding to a flip-flop. The resultingphase expression at the output of the flip-flop in FLOP is“̂M1->̂C2@LPGF:0”. The phase expressions at the inputs of module FLOP areconsistent with the phase expressions that were propagated to thecorresponding input pins of instances of FLOP. The phase expressions atthe instance output pins (i.e., ADOUT and BDOUT) are also consistentwith the phase expression at output port FQ of module FLOP. Likewise,the phase expression at the output port of module CLKGEN is consistentwith the phase expression on the output pin of the instance of CLKGEN.

The phase algebra based evaluation tool determines that inputting thecompact multi-waveform representations (e.g., phase expressions) denotedby the notations “M->A@L:0”514 and “˜G.P” 532 (which corresponds to acompact multi-waveform representation “G.P” 525 after being propagatedthrough the inverter 528) into the flip-flop module instance 524 willyield a compact multi-waveform representation with a notation of“M->G.P@TPGF:0” 542, which is the result of mapping up the phaseexpression “̂M1->̂C2@LPGF:0” using the mapping 550. The phase algebrabased evaluation tool also determines that inputting the compactmulti-waveform representations denoted by the notations “N->0:P@T” 516and “G.P” 525 into the flip-flop module instance 526 will yield acompact multi-waveform representation with a notation of “N->0:G.P@LPGF”544, which is the result of mapping up the phase expression“̂M1->̂C2@LPGF:0” using the mapping 560.

The propagation of the common sequence through the defining module ismore efficient than propagating phase expressions through a flat model.The phase expression at the output of the flip-flop (i.e., of thedefining module FLOP (602) is determined only once, instead of beingdetermined twice (once per each instance 524 and 526 of FLOP) as wouldbe done on the flat model. However, in some situations, multipleinstances of the same defining module cannot be mapped to the samemodule. In other words, there is not a single common sequence that iscommon between the multiple instances of the module, so a single phaseexpression cannot be propagated through the defining module to generatea resultant output phase expressions that can then be mapped up togenerate phase expressions for the multiple instances of the module. Inthese situations, the tool instead generates several module usages, asdescribed below.

FIG. 7 illustrates one embodiment of propagating multiple sets of phaseexpressions through multiple usages of a flip-flop module. A circuitdesign representation 702 of FIG. 7 is similar to the circuit designrepresentation 502 of FIG. 5, except that the FCLK inputs of theinstances of flip-flop modules 724 and 726 receive clock inputs that areunrelated to each other. Thus, the circuit design representation 702includes a clock generator module instance 718 and flip-flop moduleinstances 724 and 726. A net 734 is graphically depicted as connectingoutput of a primary input 710 (ADIN) to an FD input of the flip-flopmodule instance 724. A net 735 is graphically depicted as connectingoutput of a primary input 717 (ACLK) to an FCLK input of the flip-flopmodule instance 724. A net 736 is graphically depicted as connectingoutput of the primary input 712 (BDIN) to an FD input of the flip-flopmodule instance 726. A net 722 is graphically depicted as connectingoutput of the clock generator module instance 718 to an FCLK input ofthe flip-flop module instance 726.

The tool determines that the input phase expression signatures of thetwo module instances 724 and 726 are not compatible with each other. Aninput phase expression signature of a module is the phase expressionassociated with each input port of a module; i.e., it is a mapping froman input port to the phase expression. The input phase expressionsignature references a virtual clock and mode set. In one embodiment,the input phase expression signature of a module, and the virtual clockand mode map at an instance of that module are consistent with eachother if the phase expressions at the instance input pins can be mappedto the phase expressions in the signature. For example, with referenceto FIG. 6, the input phase expression signature 650 of the definingmodule FLOP (i.e., the defining module for the two instances of FLOP F1724 and F2 726) consists of phase expression “̂M1->̂C1@L:0” at input FDand phase expression “̂C2” at input FCLK. The virtual clock and mode setof the module FLOP 602 is {̂C1, ̂C2, ̂M1}.

The input phase expression signature 650 of FLOP 602 is consistent withthe instance F2:FLOP 726 because these phase expressions are consistentwith “N->0:P@T” and “G.P”, respectively, given the virtual clock andmode map 760 (i.e., the mapping 760) at instance F2. However, thesignature is not consistent with the instance F1:FLOP 724, because phaseexpression “̂C2” at input of FCLK of FLOP 802 is not consistent with thephase expression “A” at the corresponding input pin of the instanceF1:FLOP 724, as virtual clock A is mapped to virtual clock ̂C1, not ̂C2.Further, the virtual clock A cannot be mapped to ̂C2, as this wouldviolate the one-to-one mapping rule. As there is no virtual clock andmode map that would work at instance F1, the input phase expressionsignature of the defining module FLOP 802 is incompatible with theinstance F1:FLOP 724.

Thus, the tool generates two module usages to have modules with twodifferent input phase expression signatures for the module FLOP. A usageis a version of a module that can have a different set of virtualclocks, modes, and phase expressions relative to other usages of thesame module. With reference to FIG. 7, each of the instances F1:FLOP 724and F2:FLOP 726 is assigned a specific usage of the module. Thisassignment can change during the course of phase expression propagation.An input phase expression signature is then specific to a usage and itindicates a mapping from input ports of the module used by the usage tophase expressions. The virtual clocks and modes are local to a usageinstead of a module. As a result, one usage of a given module may havedifferent virtual clocks and modes than another usage of the samemodule, except that defined virtual clocks and modes are common to allusages of a module.

With reference to FIG. 8, the tool generates two usages of the moduleFLOP, usages FLOP-U1 802 and FLOP-U2 830. The input phase expressionsignature 880 of usage FLOP-U1 802 is now consistent with instanceF1:FLOP 724. The usage FLOP-U2 830 has the same input phase expressionsignature 870 as shown earlier for module FLOP, which is consistent withthe instance F2:FLOP 726. FIG. 7 illustrates the results of separatelypropagating phase expressions through the two usages, and mapping theiroutput phase expressions up to the corresponding box outputs in moduleTOP 708. The phase algebra based evaluation tool determines thatinputting the compact multi-waveform representations denoted by thenotations “M->A@L:0” 714 and “A” 719 into the flip-flop module instance724 will yield a compact multi-waveform representation with a notationof “M->A@LPGF:0” 742. The phase algebra based evaluation tool alsodetermines that inputting the compact multi-waveform representationsdenoted by the notations “N->0:P@T” 716 and “G.P” 725 into the flip-flopmodule instance 726 will yield a compact multi-waveform representationwith a notation of “N->0:G.P@LPGF” 744. The tool also generates amapping 766 for the clock generator module instance 718.

A usage of a module is compatible with an instance of that module if theinput phase expression signature of the usage is compatible with theinstance. A consistent virtual clock and mode map makes the input phaseexpression signature consistent with the instance. If the tool cansuccessfully find such a map, then the tool can reuse the results ofpropagating phase expressions through the usage for the given instancebox. One method to determine if a usage is compatible with an instanceis to iterate over all possible virtual clock and mode maps, and foreach, map the phase expressions at the instance input pins down to theusage, and see if they match the usage's input phase expressionsignature.

The tool can eliminate some usages prior to testing all of the possiblemaps. In some embodiments, if the number of distinct virtual clocksreferenced by a usage's input phase expression signature does not matchthe number of distinct virtual clocks referenced by the phaseexpressions at the instance box input pins, that usage can be rejectedas a possible candidate. A similar check can be performed for modes.

In some embodiments, the tool can compare the forms of the phaseexpressions at the instance box with the forms of the phase expressionsin the usage's input phase expression signature. To do this, the tooldefines a MIPE signature of a phase expression as a sequence ofnon-negative integers, where the ith integer in the sequence is thenumber of MIPEs found in an ROLCMP form of the phase expression thathave exactly i number of phase tags. For example, the phase expression“TST->0:B@T” has an ROLCMP form ((TST, 0), (˜TST, B@T)), which containstwo MIPEs, “0” and “B@T”, each of which contains a single phase tag. Ittherefore has a signature of (2), the sequence consisting only of theinteger 2, because it has 2 MIPEs having one phase tag. Phase expression“TST->0:A@L̂B@L”, by contrast, has ROLCMP form of ((TST, 0), (˜TST,A@L̂B@L)). This phase expression thus has a MIPE signature of (1, 1),because it has one MIPE with the single phase tag “0” and one MIPE withtwo phase tags, “A@L” and “B@L”. The phase expression “˜A” has a MIPEsignature of (1). The tool determines whether the MIPE signature of eachphase expression at the instance box inputs matches the MIPE signatureof the corresponding phase expression in the usage's input phaseexpression signature. If any do not, the usage can be rejected as acandidate.

In one embodiment, the tool generates a graph that maps virtual clocksto reject certain candidates. The tool defines a normal clock signatureof a phase expression with respect to a given virtual clock, as a set ofphase types of phase tags in the phase expression that are dependentupon the given virtual clock. The tool determines an inverse clocksignature of a phase expression with respect to a given virtual clock,as a set of phase types of the phase tags that would be produced byapplying the phase inversion function. The tool then can construct abipartite graph (referred to as a virtual clock graph), consisting oftwo sets of vertices, called set I and set U. Set I contains one vertexfor each virtual clock referenced by the phase expressions on the inputsof the instance box. Set U contains one vertex for each virtual clockreferenced by the usage's input phase expression signature. The tool cancreate an edge from a vertex in set I to a vertex in set U, if eitherthe normal clock signature for the virtual clock associated with thevertex in set I or the inverse clock signature for the virtual clockassociated with the vertex in set I is equivalent to the normal clocksignature for the virtual clock associated with the vertex in set U. Ifthe former condition is true, the edge is labeled for a normal clocksignature. If the latter condition is true, the edge is labeled for aninverse clock signature. It is possible for both conditions to be true.

Once the graph is complete, the tool can search for a perfect matching,which means a set of edges such that (1) no two edges have a commonvertex, and (2) every vertex is connected to an edge. There are knownalgorithms for finding perfect matchings. Each edge in the perfectmatching defines one or two possible virtual clock mappings. If the edgeis labeled for a normal clock signature, then the virtual clock in set Ican be mapped to the virtual clock in set U, with no inversion. If theedge is labeled for an inverse clock signature, then the virtual clockin set I can be mapped to the inverse of the virtual clock in set U. Ifthere is no perfect matching, the usage can be rejected as a candidate.Additional embodiments that limit the number of usage candidates arealso contemplated.

FIG. 9 is a flowchart of example operations for propagatingmulti-waveform representations after initialization of a circuit designrepresentation. At block 904, the circuit design representation isinitialized, such as discussed above. The flowchart of FIG. 9 can beapplied to a top level of a hierarchical design of a circuit designrepresentation (e.g., FIG. 1 TOP module 108, FIG. 5 TOP module 508,and/or FIG. 7 TOP module 708). The flowchart of FIG. 9 can be performedin a recursive fashion, as illustrated by block 9A (corresponding to theflowchart of FIG. 10) being performed if the box being accessed is not aprimitive. A primitive is an element that does not contain any othermodules, i.e., that is not a hierarchical module or module instance.When the flowchart of FIG. 9 is performed recursively, it can beperformed via the flow proceeding to block 9C 940 from blocks 1114 (FIG.11), 1208 (FIG. 12), and/or 1216.

For example, the tool can start with the TOP module 508, and thenprocesses each module instantiated in the TOP module 508, one at a time,as the tool processes each module instance. The processing of a moduleis done with respect to a particular instance encountered during theprocessing of the higher-level module, essentially using a depth-firsttraversal of a graph. Thus, FIG. 9 can be called recursively for eachmodule usage in the hierarchical module TOP 508. In one embodiment, withreference to pseudocode discussed below, the flowchart of FIG. 9corresponds to propagate_through_usage function.

At block 908, a source set is checked to determine whether it is empty.If the source set is empty, then the propagation process is complete andthe flow proceeds to block 936. At block 936, checking is applied to theresulting multi-waveform representation propagated throughout thedesign. The checking algorithms use the generated phase ids to identifyparticular characteristics associated with a design, some of which canbe potential defects. If the source set was not empty at block 908, theflow proceeds to block 911.

At block 911, the tool determines whether the next box in the source setis a primitive box. If the box is a primitive box, the flow proceeds toblock 912A. If the box is not a primitive box (i.e., the box is aninstance box that corresponds to a module instance), the flow proceedsto block 913 (i.e., element 9A via which the flow proceeds to theflowchart of FIG. 10).

At block 912A, an input multi-waveform representation is propagatedthrough the next box in a source set and the processed box is removedfrom the source set. The flow proceeds to block 912A from block 911. Inone embodiment, block 912A can be called (e.g., called in a mannersimilar to that of a function or a subroutine) from block 911. At block912A, the input multi-waveform representation is propagated through thebox by applying operators such as those of FIG. 2. For example, an inputphase id is used to search for a result phase id in a lookup table. If aresult phase id is found in the lookup table, then the result phase idis returned, and the process proceeds to block 912B. The particular lookup tables accessed will vary dependent upon the phase id and theoperation (e.g., AND, OR, etc.) represented by the box. However, if aresult phase id is not found in the lookup table, then the input phaseid is converted to a ROLCMP in accordance with the phase id look-upalgorithm. Operations then can be performed on the ROLCMPs. Phaseexpressions can be derived from the ROLCMP operations. The phaseexpressions can be converted into phase ids. At block 912B, theprocessed box is removed from the source set. The flow can proceed toblock 912B from block 912A or from block 915 (i.e., element 9B). Theprocess proceeds to block 916.

At block 916, the multi-waveform representation resulting from block 912is compared to the multi-waveform representation currently associatedwith the output net of the processed box. If the resultingmulti-waveform representation is different from the currentmulti-waveform representation, the flow proceeds to block 920.Otherwise, the process proceeds to block 928.

At block 920, the multi-waveform representation resulting from block 912is assigned to the output net associated with the processed box. Atblock 924, the sink boxes of the net are placed in the update set.

At block 928, the source set is checked to determine whether it isempty. If the source set is not empty, then the flow again proceeds toblock 911 at which the next box in the source set is processed.Otherwise, the flow proceeds to block 932. At block 932, the source setis overwritten with the contents of the update set. The flow proceeds toblock 908.

FIG. 10 is a flowchart of example operations for propagatingmulti-waveform representations (e.g., phase expressions) throughhierarchical modules, or module usages.

At block 1002, the flowchart of FIG. 10 is accessed from block 9A ofFIG. 9. With reference to FIG. 5, the tool can access module instanceF1:FLOP 524, as the first box being processed by the flowchart of FIG. 9(i.e., after processing the module TOP) that is a hierarchical box;i.e., a module instance.

At block 1004, the tool determines whether the defining module of themodule instance that is currently being processed is associated withmultiple instances. In one embodiment, the tool can determine if thereare any instances of the module that have already been processed. Inanother embodiment, the tool can determine if there are multipleinstances of the module in the circuit design representation, regardlessof whether the other instances have been processed. With reference toFIG. 5 as an example, the tool determines whether the defining module ofmodule instance F1:FLOP 524 is associated with multiple instances.Depending on the implementation, the tool can determine whether themodule instance F2:FLOP 526 has already been processed, or will beprocessed. If the module is associated with multiple instances, i.e., ifthere are two or more instances of a given module in the same parentmodule (i.e., in the parent module TOP) of the current design, then theflow proceeds to block 1008. If the module is not associated withmultiple instances, then the flow proceeds to block 1010 (i.e., themethod of FIG. 11 via block “10A”).

At block 1008, the tool determines whether the two instances of the samemodule share a common usage. The tool can make this determination is avariety of ways, such as by determining whether module instances of aregister transfer level circuit design share a common usage, eachinstance being associated with a mapping. The two instances (e.g., F1and F2) share the common usage if a sequence of signal transitionrepresentations received by the first instance can be mapped using afirst mapping to the same common sequence of signal transitionrepresentations as a mapping of another sequence of signal transitionrepresentations received by the second instance using a second mapping.In one embodiment, during this determination, the tool also maps downthe phase expression as received by the current instance to the inputsof the previously generated usage. If the tool determines that the firstand second instances do not share a common usage, then the flow proceedsto block 1010 (i.e., the method of FIG. 11 via block “10A”). If the tooldetermines that the first and second instances share the common usage,then the flow proceeds to block 1012.

In one embodiment, instead of the determinations of blocks 1004 and1008, the tool determines whether there is an existing usage of thedefining module that is compatible with the first instance. The tool cantest every existing usage (if any exist) of the defining module. Thus,with reference to FIG. 5 as an example, the tool can determine whetherthere is an existing usage of the defining module (e.g., FLOP 602) isthat compatible with the first instance 524. If the tool determines thatthere is a compatible usage, then the flow proceeds to block 1012. Ifthe tool determines that there is not a compatible usage, then the flowproceeds to block 1010.

At block 1012, the tool accesses the previously generated common usage.At block 1014, the tool updates the previously generated common usage.With reference to FIGS. 5 and 6, the tool can update any data structuresassociated with the common usage of FLOP module 602, including anindication that both F1:FLOP 524 and F2:FLOP 526 share the same usage.

At block 1016, the tool propagates the phases up using results of thephase expressions previously propagated through the common usage. Sincethe phase expression of the instance being processed does not need to bepropagated through the common usage, the tool uses the results of aprevious propagation (i.e., the propagation through the common usagethat was previously performed for the second instance of the module) anduses the mappings (i.e., the mappings 550) to generate the phaseexpression for the output e.g., ADOUT 542. Once block 1016 is performed,the flow proceeds to block 1020 (i.e., to block 9B which corresponds toblock 915 of FIG. 9). Block 1020 can also be accessed by block 10B 1018(e.g., that is called from the flowchart of FIG. 11).

FIG. 11 is a flowchart of example operations for propagatingmulti-waveform representations through hierarchical modules.

At block 1104, the flowchart of FIG. 1 is accessed from block 10A ofFIG. 10. At block 1106, the tool determines whether the first instanceof the module has a previous assignment. With reference to FIG. 7 as anexample, the tool determines whether F1:FLOP 724 has a previousassignment. The F1:FLOP 724 module has a previous assignment if there isa separate usage previously created for F1:FLOP 724 (i.e., differentfrom usage 830 for F2:FLOP 726). If the first instance of the module hasa previous assignment, then the flow proceeds to block 1108 (blocklabelled 11A which corresponds to performing the flowchart of FIG. 12).If the first instance does not have a previous assignment, then the flowproceeds to block 1110.

At block 1110, the tool generates an initial usage for the firstinstance. With reference to FIGS. 7 and 8 as examples, the toolgenerates FLOP-U1 usage, as FLOP-U2 usage is the other usage for theFLOP module that is not a common usage between the F1:FLOP 724 andF2:FLOP 726 instances of the FLOP module. Furthermore, the toolgenerates mappings 750 for the first instance.

At block 1112, the phases are propagated down to the initial usage. Withreference to FIGS. 7 and 8, the phase expression “M->A@L:0” 714 ismapped down to the first usage 802 using the mappings 750. The mappeddown phase expression is then ready to be propagated through the firstusage 802.

At block 1114, the mapped down phase expression for the initial usage ispropagated through the initial usage by recursively performing block 9Cof FIG. 9. Thus, the flowchart of FIG. 9 can be called recursively foreach hierarchical module being processed. The resultant propagated phaseexpression is output on the port 810 of the first usage 802.

At block 1116, the resultant propagated phase expression is then mappedup out of the initial usage. Thus, the resultant propagated phaseexpression is mapped up from the first usage 802 using mappings 750 toADOUT of “M->A@LPGF:0” 742. Once block 1116 is performed, the flowproceeds to block 1120 (i.e., to block 10B which corresponds to block1018 of FIG. 10). Block 1120 can also be accessed by block 11B 1118 thatis called from the flowchart of FIG. 12.

FIG. 12 is a flowchart of example operations for propagatingmulti-waveform representations through hierarchical modules.

At block 1201, the flowchart of FIG. 12 is accessed from block 11A ofFIG. 11. At block 1202, the tool determines whether the previouslyassigned usage is shared. With reference to FIGS. 7 and 8, the tooldetermines whether the first usage 802 is shared with another instance(e.g., by a different instance from F2:FLOP instance 726). If the tooldetermines that the first usage is shared with another instance, theflow proceeds to block 1204. If the tool determines that the first usageis not shared with another instance, the flow proceeds to block 1214.

At block 1204, the tool generates a clone usage of the previouslyassigned usage. Thus, the tool generates a clone usage FLOP-U1-CLONE 850of the first usage 802. The clone usage 850 is generated such that anysubsequent changes to the first usage 802 would not affect phaseexpressions that have been already propagated through the clone usage850. In other words, any subsequent changes to clone 850 will not affectthe first usage 802.

At block 1206, the phases are propagated down to the clone usage. Withreference to FIGS. 7 and 8, the phase expression “M->A@L:0” 714 ismapped down to the clone usage 850 using the mappings 750. The resultantmapped down phase expression is then ready to be propagated through theclone usage 850.

At block 1208, the mapped down phase expression is propagated throughthe clone usage by performing block 9C of FIG. 9. Thus, the flowchart ofFIG. 9 can be called recursively for each hierarchical module beingprocessed. The resultant propagated phase expression is output on theports of the clone usage 850.

At block 1210, the resultant propagated phase expression is mapped upout of the clone usage. Thus, the resultant propagated phase expressionis mapped up from the clone usage 850 using mappings 750 to ADOUT 742 of“M->A@LPGF:0”. Once block 1210 is performed, the flow proceeds to block1220 11B (i.e., to block 1020 of FIG. 10).

If the tool determines that the previously assigned usage is not shared,then blocks 1214-1218 are performed instead of blocks 1204-1210. Blocks1214-1218 are similar to blocks 1206-1210, except that whereas blocks1214-1218 operate on an existing non-shared usage, blocks 1206-1210operate on a clone usage of the existing shared usage. Furthermore,blocks 1214-1218 are similar to blocks 1112-1116, except that whereasblocks 1214-1218 operate on an existing non-shared usage (i.e., thepreviously assigned usage), blocks 1112-1116 operate on an initial usageof a module instance.

At block 1214, the phases are propagated down to the non-shared usage.With reference to FIGS. 7 and 8, the phase expression “M->A@LPGF:0” 714is mapped down to the non-shared (i.e., previously assigned) usage 802using the mappings 750. The resultant mapped down phase expression isthen ready to be propagated through the non-shared usage 802.

At block 1216, the mapped down phase expression is propagated throughthe non-shared usage by performing block 9C of FIG. 9. Thus, theflowchart of FIG. 9 can be called recursively for each hierarchicalmodule being processed. The resultant propagated phase expression isoutput on the ports of the non-shared usage 802.

At block 1218, the resultant propagated phase expression is then mappedup out of the non-shared usage. Thus, the resultant propagated phaseexpression is mapped up from the non-shared usage 802 using mappings 750to ADOUT 742 of “M->A@LPGF:0”. Once block 1218 is performed, the flowproceeds to block 1220 11B (i.e., to block 1020 of FIG. 10).

In some embodiments, the propagation algorithm described above withreference to FIGS. 10-12 is divided into the following six namedprocedures.

create_initialized_usage record_phase_id propagate_through_usagepropagate_through_instance_box propagate_phases_down propagate_phases_up

Each procedure is listed in a section below. In some embodiments, theprocedures operate on associative data structures (data objects) thatstore data associated with the circuit design. An associative datastructure stores data values that are each associated with a unique key.The procedures use the syntax associative_data_structure [key] to referto the data value associated with the given key. A key may be compound,meaning, that it consists of a sequence of values. In the procedurelistings, the term “iff” means “if and only if”, and the characters “//”precede a comment. The algorithm is performed on a given hierarchicaldesign by the following two-step pseudocode, which calls two of thenamed procedures:

Let top_usage_id = create_initialized_usage ( top_level_module ). Callpropagate_through_usage ( top_usage_id ).

The propagate_through_usage procedure indirectly recursively callsitself for all the underlying usages in the design, propagating phaseexpressions through each. At the completion of the above pseudocode,phase expressions will be propagated to all nets in the hierarchicaldesign.

Procedure create_initialized_usage—the following procedure creates a newusage of a module, and initializes the phase IDs for all nets in themodule. It returns the ID of the new usage.

procedure create_initialized_usage formal argument: module_id returns:new usage_id { Let usage_id = a new, unused usage ID for the modulereferenced by module_id. for each instance box in the module referencedby module_id { // Mark instance box as updated so it will be assigned ausage. Add instance box to module_updated_boxes [ module_id ]. } foreach net in the module referenced by module_id { if ( net is driven bytie-down or tie-up ) { Let phase_expr = “0” or “1”, respectively. } elseif ( net has been assigned a phase expression by the designer ) { Letphase_expr = the given phase expression. For each virtual clock and modereferenced by phase_expr, add it to usage_vitutal_clocks [usage_id] orusage_modes [usage_id], respectively. } else if ( net is connected to aninput port and module_id refers to the top-level module ) { Letphase_expr = “<>”, } else if ( net is connected to the output of a clockgenerator ) } Let phase_expr = “<>”. } else { Let phase_expr = “-”. }Call record_phase_id ( usage_id, net, phase ID corresponding tophase_expr ). } // end for each net Return usage_id. } // end procedurecreate_intialized_usage

Procedure record_phase_id—the following procedure is called whenever thephase ID assigned to a net is initialized or potentially updated. Thenet argument refers to one net (signal) within the module used by theusage_id argument. The purpose of this procedure is not only to recordthe net's phase ID, but to mark any downstream boxes or ports which maybe affected by the net's update, so that they will subsequently beprocessed. The term “sink box” is used to mean any box (primitivecomponent or instance box) that has an input pin connected to the givennet.

procedure record_phase_id formal arguments: usage_id, net, phase_id {Let module_id = ID of module used by usage_id (which contains the givennet). Let Boolean flag is_update = false. if ( usage_net_phase_id[usage_id, net ] has not been initialized ) { Set usage_net_phase_id [usage_id, net ] equal to phase_id. Set is_update = true if phase id_isnot the phase ID for “-”. } else if ( usage_net_phase_id [ usage_id, net] stores a value other than phase_id ) { if ( net was assigned a phaseexpression by the designer ) {// Leave phase ID assigned to netunchanged, but store conflict (to report error). Setusage_net_phase_id_conflict [ usage_id, net ] equal to phase_id. } else{ Set usage_net_phase_id [ usage_id, net ] equal to phase_id. Setis_update = true. } } if ( is_update is true ) { for each sink box ofnet { Add sink box to module_updated_boxes [ module-id ]. if ( sink boxis an instance box ) { Let input_pin = pin of instance box connected tonet. Add input_pin to module_updated_instance_pins [ module_id, sink box]. } } // end for each sink box if ( net is connected to an output portof the module referenced by module_id ) { Add output port tomodule_updated_output_ports [ module_id ]. Set usage_port_phase_id [usage_id, output port ] equal to phase_id. } } } // end procedurerecord_phase_id

Procedure propagate_through_usage—the following procedure will propagatephase IDs through the specified usage, and will indirectly recursivelycall itself for each child usage, via the call topropagate_through_instance_box.

procedure propagate_through_usage formal argument: usage_id { Letmodule_id = ID of module used by usage_id. // Propagate updates fromabove (via input ports), if any. for each input_port inmodule_updated_input_ports [ module_id ] { Call record_phase_id (usage_id, net connected to input_port. usage_port_phase_id [ usage_id,input_port ] ). } Set module_updated_input_ports [ module_id ] equal tothe empty set. // Propagate from boxes updated by initialization, andpropagation from input ports. Let source_set = module_updated_boxes [module_id ]. while ( source_set is not empty ) { Setmodule_updated_boxes [ module_id ] to the empty set. for each box insource_set { if (box is primitive box) { Let phase_id = the phase IDevaluated for the box output as a func-tion of the phase IDs assigned,to its input nets // (stored in usage_net_phase_id) Call record_phase_id( usage_id, net connected to box output. phase_id ). else { // box isinstance box Call propagate_through_instance_box ( usage_id, box ). } }// end for Set source_set equal to module_updated boxes [ module_id ]. }// end while } // end procedure propagate_through_usage

Procedure propagate_through_instance_box—the following sub-procedure iscalled by the previous propagation procedure to propagate phase IDsthrough an instance box. It in turn calls the previous procedure(indirect recursion) for the usage ID assigned to the instance box.

procedure propagate_through_instance_box formal arguments: usage_id,instance_box { Let module_id = ID of instantiating module ofinstance_box (module used by usage_id.) Let child_module_id = ID ofdefining module of instance_box. Test each existing usage of modulechild_module_id for compatibility with instance_box if ( found acompatible usage (and therefore a consistent virtual clock and mode map)) { Set usage_instance_box_usage [usage_id, instance_box] to thecompatible usage's ID. for each virtual_clock_or_mode_name referenced byinstance_box input phase expressions { Set usage_instance_box_map[usage_id, instance_box, vir- tual_clock_or_mode_name] to thelower-level virtual clock or mode, or its inversion, that was assignedby the consistent map found for the compati-ble usage (which may be anextension of a previous map, in which case some values will not change).} Set module_updated_instance_pins [ module_id, instance_box ] to theempty set. Add all output ports of child_module tomodule_updated_output_ports [ child_module_id ]. } else { // There is noexisting usage compatible with instance_box. if ( there is no usagealready assigned to instance_box ) { Let child_usage_id =create_initialized_usage (child_module_id). Set usage_instance_box_usage[usage_id, instance_box ] = child_usage_id. } else { Let child_usage_id= usage_instance_box_usage [usage_id, in-stance_box]. if (child_usage_id is assigned to (shared by) any other instance in thede-sign ) { Create a clone of child_usage_id by copying all data forchild_us-age_id to a new previously unused usage ID for modulechild_module_id (see below). Set usage_instance_box_usage [usage_id,instance_box] to the ID of the clone. Set child_usage_id to the ID ofthe clone. } } Call propagate_phases_down ( usage_id, instance_box,child_usage_id ). Recursively call propagate_through_usage (child_usage_id ). } Call propagate_phases_up ( usage_id, instance_box,child_usage_id ). } // end procedure propagate_through_instance_box

In one implementation, the copying all data means that, for each of thefollowing data objects, for any entry indexed (in part) by thechild_usage_id, the tool creates a duplicate entry that is insteadindexed by the new, previously unused ID:

usage_virtual_clocks usage_modes usage_instance_box_usageusage_instance_box_map usage_net_phase_id usage_net_phase_id_conflictusage_port_phase_id

However, if no compatible usage is found, then no two instances of amodule will share a usage.

Procedure propagate_phases_down—the following sub-procedure is called bypropagate_through_instance_box to propagate phase IDs from the inputs ofan instance box to the input ports of its assigned usage.

procedure propagate_phases_down formal arguments: usage_id,instance_box, child_usage_id { Let module_id = ID of instantiatingmodule of instance_box (module used by usage_id). Let child_module_id =ID of defining module of instance_box (module used by child_usage_id).for each input_pin in module_updated_instance_pins [ module_id,instance_box ] { Let phase_id = usage_net_phase_id [ usage_id, netconnected to input_pin ]. Let child_input_port = input port ofchild_module corresponding to input_pin. for eachvirtual_clock_or_mode_name referenced by phase_id. { if (virtual_clock_or_mode_name has not been mapped for this instance box ) {Let from_above_name = next available from-above name for child_usage_id// (e.g., {circumflex over ( )}C1, {circumflex over ( )}C2, for virtualclocks; {circumflex over ( )}M1, {circumflex over ( )}M2, for modes).Add from_(——)above_name to usage_virtual_clocks [child_usage_id] orusage_modes [child_usage_id], as appropriate. Set usage_instance_box_map[usage_id, instance_box, vir-tual_clock_or_mode_name] = from_above_name.} } Let child_phase_id = mapping of phase_id down to the child usage Setusage_port_phase_id [ child_usage_id, child_input_port ] equal tochild_phase_id. Add child_input_port to module_updated_input_ports [child_module_id ]. } Set module_updated_instance_pin [ module_id,instance_box ] to the empty set. } // end procedurepropagate_phases_down

Procedure propagate_phases_up—the following sub-procedure is called bypropagate_through_instance_box to propagate phase IDs from the outputports of the usage assigned to an instance box, to the nets connected tothe outputs of the instance box.

procedure propagate_phases_up formal arguments: usage_id, instance_box,child_usage_id { Let child_module_id = ID of defining module ofinstance_box (module used by child_us-age id). for each child_ouput_portin module_updated_output_ports [ child_module_id ] { Let child_phase_id= usage_port_phase_id [ child_usage_id, child_output_port ]. for eachchild_virtual_clock_or_mode_name referenced by child_phase_id that hasnot been mapped for this instance box (thus has origin of from_currentor from_below) { Let from_below_name = virtual clock or mode name forusage_id, corre-sponding to child_virtual_clock_or_mode_name (prependedwith instance name if virtual clock or mode originates from below) Addfrom_below_name to usage_virtual_clocks [usage_id] or us-age modes[usage_id], as appropriate. Set usage_instance_box_map [usage_id,instance_box, from_be-low_name] = child_virtual_clock_or_mode_name. }Let phase_id = mapping of child_phase_id_up to the current usage(usage_id) Let output_net = net connected to output pin of instance_boxcorresponding to child_output_port. Call record_phase_id ( usage_id,output_net, phase_id ). } Set module_updated_output_ports [child_module_id ] to the empty set } // end procedurepropagate_phases_up

FIG. 13 depicts an example computer system compact multi-wave basedcircuit design evaluator. A computer system includes a processor unit1304 (possibly including multiple processors, multiple cores, multiplenodes, and/or implementing multi-threading, etc.). The computer systemincludes a memory unit 1308. The memory unit 1308 may be system memory(e.g., one or more of cache, SRAM, DRAM, zero capacitor RAM, TwinTransistor RAM, eDRAM, EDO RAM, DDR RAM, EEPROM, NRAM, RRAM, SONOS,PRAM, etc.) or any one or more of the above already described possiblerealizations of machine-readable media. The computer system alsoincludes a bus 1312 (e.g., PCI bus, ISA bus, PCI-Express bus,HyperTransport® bus, InfiniBand® bus, NuBus, etc.). The computer systemalso includes a compact multi-wave based circuit design evaluator(“evaluator”) 1321. The evaluator propagates compact representations ofmultiple waveforms throughout nets of a register level circuit designrepresentation as previously described. The memory unit 1308 may includeone or more functionalities that facilitate storing the look-up tablesor other data structures for evaluating a circuit design representationbased on representations of multiple waveforms and decomposition ofcompact multi-waveform representations into sequence of nondeterministicsignal transition representations. Any one of these functionalities maybe partially (or entirely) implemented in hardware and/or on theprocessor unit 1304. For example, the functionality may be implementedwith an application specific integrated circuit, in logic implemented inthe processor unit 1304, in a co-processor on a peripheral device orcard, etc. The processor unit 1304 and the memory unit 1308 are coupledto the bus 1312. Although illustrated as being coupled to the bus 1312,the memory unit 1308 may be coupled to the processor unit 1304.

While the embodiments are described with reference to variousimplementations and exploitations, it will be understood that theseembodiments are illustrative and that the scope of the inventive subjectmatter is not limited to them. In general, techniques for evaluating aregister level circuit design representation with compact multi-waveformrepresentations as described herein may be implemented with facilitiesconsistent with any hardware system or hardware systems. Manyvariations, modifications, additions, and improvements are possible.

Plural instances may be provided for components, operations orstructures described herein as a single instance. Finally, boundariesbetween various components, operations and data stores are somewhatarbitrary, and particular operations are illustrated in the context ofspecific illustrative configurations. Other allocations of functionalityare envisioned and may fall within the scope of the inventive subjectmatter. In general, structures and functionality presented as separatecomponents in the example configurations may be implemented as acombined structure or component. Similarly, structures and functionalitypresented as a single component may be implemented as separatecomponents. These and other variations, modifications, additions, andimprovements may fall within the scope of the inventive subject matter.

What is claimed is:
 1. A method comprising: determining a first mappingassociated with a first instance of a first module of a register levelcircuit design and a second mapping associated with a second instance ofthe first module, wherein the first mapping is for mapping a first inputsequence of signal transition representations received by the firstinstance to a common sequence of signal transition representations, andthe second mapping is for mapping a second input sequence of signaltransition representations received by the second instance to the commonsequence; determining whether the first instance and the second instanceshare a common usage, wherein the common usage is associated with aresult sequence of signal transition representations that was generatedby a previous propagation of the common sequence through the commonusage, and each signal transition representation represents anon-deterministic transition from a previous signal state to a set ofone or more possible signal states; and in response to determining thatthe first instance and the second instance share the common usage,mapping the result sequence of signal transition representations to anoutput sequence of signal transition representations for the secondinstance using the second mapping.
 2. The method of claim 1, wherein theprevious propagation of the mapped first input sequence comprises,propagating the common sequence through the common usage to generate theresult sequence of signal transition representations, wherein the resultsequence of signal transition representations is for mapping to a firstoutput sequence of signal transition representations for the firstinstance using the first mapping, and the result sequence of signaltransition representations is for mapping to a second output sequence ofsignal transition representations for the second instance using thesecond mapping.
 3. The method of claim 1, wherein the first mapping mapsone or more of: a clock of the first input sequence to a clock of thecommon sequence, and a mode of the first input sequence to a mode of thecommon sequence.
 4. The method of claim 1, wherein the common sequenceis generated based on the first mapping prior to said determiningwhether the first instance and the second instance share the commonusage.
 5. The method of claim 1, wherein said determining whether thefirst instance and the second instance share the common usage comprises,determining a plurality of second mapping candidates for mapping thesecond input sequence to the common sequence, and determining the secondmapping from the plurality of second mapping candidates.
 6. The methodof claim 5, further comprising, eliminating one or more of the pluralityof second mapping candidates prior to said determining the secondmapping from the plurality of second mapping candidates.
 7. The methodof claim 1, further comprising: in response to determining that thefirst instance and the second instance do not share the common usage,determining whether the second instance is associated with an existingassignment of another usage of the first module; and in response todetermining that the second instance is not associated with the existingassignment of another usage, generating an initial usage of the firstmodule, mapping the second input sequence to an initial sequence ofsignal transition representations using an initial mapping, andpropagating the initial sequence through the initial usage to generatean initial result sequence of signal transition representations.
 8. Themethod of claim 7, further comprising: in response to determining thatthe second instance is associated with the existing assignment ofanother usage, determining whether the another usage is shared withanother instance of the first module; and in response to determiningthat the another usage is shared, generating a clone usage of theanother usage, mapping the second input sequence to a clone sequence ofsignal transition representations using a clone mapping, and propagatingthe clone sequence through the clone usage to generate a clone resultsequence of signal transition representations.
 9. The method of claim 8,further comprising: in response to determining that the another usage isnot shared, mapping the second input sequence to a shared sequence ofsignal transition representations using a third mapping, and propagatingthe shared sequence through a shared usage to generate a shared resultsequence of signal transition representations.
 10. A computer programproduct for evaluating a circuit design, the computer program productcomprising: a computer readable storage medium having programinstructions stored thereon, the program instructions comprising programinstructions to, determine a first mapping associated with a firstinstance of a first module of a register level circuit design and asecond mapping associated with a second instance of the first module,wherein the first mapping is for mapping a first input sequence ofsignal transition representations received by the first instance to acommon sequence of signal transition representations, and the secondmapping is for mapping a second input sequence of signal transitionrepresentations received by the second instance to the common sequence;determine whether the first instance and the second instance share acommon usage, wherein the common usage is associated with a resultsequence of signal transition representations that was generated by aprevious propagation of the common sequence through the common usage,and each signal transition representation represents a non-deterministictransition from a previous signal state to a set of one or more possiblesignal states; and in response to determining that the first instanceand the second instance share the common usage, map the result sequenceof signal transition representations to an output sequence of signaltransition representations for the second instance using the secondmapping.
 11. The computer program product of claim 10, wherein theprevious propagation of the mapped first input sequence comprises,propagation of the common sequence through the common usage to generatethe result sequence of signal transition representations, wherein theresult sequence of signal transition representations is for mapping to afirst output sequence of signal transition representations for the firstinstance using the first mapping, and the result sequence of signaltransition representations is for mapping to a second output sequence ofsignal transition representations for the second instance using thesecond mapping.
 12. The computer program product of claim 10, whereinthe first mapping maps one or more of: a clock of the first inputsequence to a clock of the common sequence, and a mode of the firstinput sequence to a mode of the common sequence.
 13. The computerprogram product of claim 10, wherein the common sequence is generatedbased on the first mapping prior to the determination of whether thefirst instance and the second instance share the common usage.
 14. Thecomputer program product of claim 10, wherein program instructions todetermine whether the first instance and the second instance share thecommon usage comprise program instructions to, determine a plurality ofsecond mapping candidates for mapping the second input sequence to thecommon sequence, and determine the second mapping from the plurality ofsecond mapping candidates.
 15. The computer program product of claim 14,further comprising program instructions to, eliminate one or more of theplurality of second mapping candidates prior to said determining thesecond mapping from the plurality of second mapping candidates.
 16. Anapparatus comprising: a processor; and a computer readable storagemedium having stored thereon program instructions executable by theprocessor to cause the apparatus to, determine a first mappingassociated with a first instance of a first module of a register levelcircuit design and a second mapping associated with a second instance ofthe first module, wherein the first mapping is for mapping a first inputsequence of signal transition representations received by the firstinstance to a common sequence of signal transition representations, thesecond mapping is for mapping a second input sequence of signaltransition representations received by the second instance to the commonsequence; determine whether the first instance and the second instanceshare a common usage, wherein the common usage is associated with aresult sequence of signal transition representations that was generatedby a previous propagation of the common sequence through the commonusage, and each signal transition representation represents anon-deterministic transition from a previous signal state to a set ofone or more possible signal states; and in response to determining thatthe first instance and the second instance share the common usage, mapthe result sequence of signal transition representations to an outputsequence of signal transition representations for the second instanceusing the second mapping.
 17. The apparatus of claim 16, wherein theprevious propagation of the mapped first input sequence comprises,propagation of the common sequence through the common usage to generatethe result sequence of signal transition representations, wherein theresult sequence of signal transition representations is for mapping to afirst output sequence of signal transition representations for the firstinstance using the first mapping, and the result sequence of signaltransition representations is for mapping to a second output sequence ofsignal transition representations for the second instance using thesecond mapping.
 18. The apparatus of claim 16, wherein the first mappingmaps one or more of: a clock of the first input sequence to a clock ofthe common sequence, and a mode of the first input sequence to a mode ofthe common sequence.
 19. The apparatus of claim 16, wherein the commonsequence is generated based on the first mapping prior to thedetermination of whether the first instance and the second instanceshare the common usage.
 20. The apparatus of claim 16, wherein programinstructions executable to determine whether the first instance and thesecond instance share the common usage comprise program instructionsexecutable to, determine a plurality of second mapping candidates formapping the second input sequence to the common sequence, and determinethe second mapping from the plurality of second mapping candidates.